Asymptotically vanishing nodal solutions for critical double phase problems

Article type: Research Article

Authors: Liu, Zhenhai^{a; b; *} | Papageorgiou, Nikolaos S.^c

Affiliations: [a] Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi, 530006, P.R. China | [b] Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, P.R. China | [c] Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece. E-mail: npapg@math.ntua.gr

Correspondence: [*] Corresponding author. E-mail: zhhliu@hotmail.com.

Abstract: We consider a Dirichlet double phase problem with unbalanced growth. In the reaction we have the combined effects of a critical term and of a locally defined Carathéodory perturbation. Using cut-off functions and truncation techniques we bypass the critical term and deal with a coercive problem. Using this auxillary problem, we show that the original Dirichlet equation has a whole sequence of nodal (sign-changing) solutions which converge to zero in the Musielak–Orlice–Sobolev space and in L∞.

Keywords: Double phase integrand, unbalanced growth, Musielak–Orlice spaces critical term, nodal solutions, cut-off function

DOI: 10.3233/ASY-201645

Journal: Asymptotic Analysis, vol. 124, no. 3-4, pp. 291-302, 2021